Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Equation of the Diameter of the Circle X2 + Y2 − 2x + 4y = 0 Which Passes Through the Origin is - Mathematics

MCQ

Equation of the diameter of the circle x2 + y2 − 2x + 4y = 0 which passes through the origin is

#### Options

• x + 2y = 0

• x − 2y = 0

• 2x + y = 0

• 2x − y = 0Let the diameter of the circle be y = mx.
Since the diameter of the circle passes through its centre, (1, −2) satisfies the equation of the diameter.

#### Solution

2x + y = 0

Let the diameter of the circle be y = mx.
Since the diameter of the circle passes through its centre, (1, −2) satisfies the equation of the diameter.

∴ $m = - 2$

Substituting the value of m in the equation of diameter:

$y = - 2x$
$\Rightarrow 2x + y = 0$
Hence, the required equation of the diameter is
$2x + y = 0$.
Concept: Circle - Standard Equation of a Circle
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Q 23 | Page 40